On Free Topological Groups with the Inductive Limit Topologiesa
Ol'ga Viktorovna Sipacheva · Annals of the New York Academy of Sciences · 1996
ABSTRACT Countable spaces with an only nonisolated point for which the free topological groups are the inductive limits of the sets of words having restricted length are characterized. It is proved for a collectionwise normal X that if its free topological group is the inductive limit of the sets of words having restricted length, then any closed discrete set of non‐P‐points in X is countable. All the results obtained are valid for both Abelian and non‐Abelian free groups.